You can download a copy of the Easter activities guide from Southwark Council's website here - loads of free and fun things to do. Probably a bit early for summer, but it's also worth having a look at the family activities pages.
I dont know what age things start at the Unicorn but they offer some wonderful opportunities for young people interested in drama. Worth checking out for the longer term.
Stagecoach? Don't know where the nearest branch is - my kids are not drama types, but I know that this is something that some of their friends have done.
Try also the Families website. I sometimes pick up the Families South West Magazine and it seems to have loads of adverts for just about every holiday course including drama. There is supposed to be a Families South East as well but in 14 years of being a local parent I have never potted a copy. I assume it is more about Dulwich.